Starting with polynomial:
P : 16*t^5 - 20*t^3 + 5*t
Extension levels are: 5 36 40
-------------------------------------------------
Trying to find an order 36 Kronrod extension for:
P1 : 16*t^5 - 20*t^3 + 5*t
Solvable: 1
-------------------------------------------------
Trying to find an order 40 Kronrod extension for:
P2 : 16*t^41 - 168*t^39 + 818*t^37 - 2451*t^35 + 10115/2*t^33 - 30481/4*t^31 + 138787/16*t^29 - 243629/32*t^27 + 21352149/4096*t^25 - 22931025/8192*t^23 + 38629305/32768*t^21 - 25398555/65536*t^19 + 25820145/262144*t^17 - 9992005/524288*t^15 + 5757475/2097152*t^13 - 1196069/4194304*t^11 + 5475173/268435456*t^9 - 503481/536870912*t^7 + 53333/2147483648*t^5 - 1335/4294967296*t^3 + 5/4294967296*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 16*t^81 - 328*t^79 + 3238*t^77 - 20501*t^75 + 748325/8*t^73 - 5242641/16*t^71 + 58666377/64*t^69 - 269253939/128*t^67 + 2066445557/512*t^65 - 6724376945/1024*t^63 + 37510410223/4096*t^61 - 90412119473/8192*t^59 + 758074648799/65536*t^57 - 1388647909691/131072*t^55 + 4462127961615/524288*t^53 - 6304519296045/1048576*t^51 + 1004471202260565/268435456*t^49 - 1102606665411405/536870912*t^47 + 2135390661379815/2147483648*t^45 - 1823451793911825/4294967296*t^43 + 5486885897842965/34359738368*t^41 - 3630225306480465/68719476736*t^39 + 4214986347647985/274877906944*t^37 - 2140586247441915/549755813888*t^35 + 3789443170401525/4398046511104*t^33 - 1454693706607869/8796093022208*t^31 + 963279451051883/35184372088832*t^29 - 273214376948261/70368744177664*t^27 + 263374723516751/562949953421312*t^25 - 53406232536475/1125899906842624*t^23 + 18010091821799/4503599627370496*t^21 - 2489098783589/9007199254740992*t^19 + 17729302242597/1152921504606846976*t^17 - 1554115724493/2305843009213693952*t^15 + 208607759535/9223372036854775808*t^13 - 10327828537/18446744073709551616*t^11 + 1433973073/147573952589676412928*t^9 - 32436781/295147905179352825856*t^7 + 853333/1180591620717411303424*t^5 - 5335/2361183241434822606848*t^3 + 5/2361183241434822606848*t
-------------------------------------------------
Computing nodes and weights
  current precision for roots: 53
  current precision for roots: 106
  current precision for roots: 212
 current precision for weights: 53
Linear system for weights solvable: 0
  current precision for roots: 106
  current precision for roots: 212
 current precision for weights: 106
Linear system for weights solvable: 0
  current precision for roots: 212
  current precision for roots: 424
 current precision for weights: 212
Linear system for weights solvable: 0
  current precision for roots: 424
  current precision for roots: 848
 current precision for weights: 424
Linear system for weights solvable: 1
  current precision for roots: 848
  current precision for roots: 1696
 current precision for weights: 848
Linear system for weights solvable: 1
Sufficient bits for target precision reached
Positive weights:   81 out of 81
Indefinite weights: 0 out of 81
Negative weights:   0 out of 81
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (-0.98078528040323044913 + 1.7990952677570151978e-1662j)  +/-  (1.93e-480, 1.93e-480j)
| (-0.97236992039767660183 + 6.8894573933905935503e-1670j)  +/-  (1.19e-480, 1.19e-480j)
| (-0.93819133592248413445 + 2.8144931073112819389e-1678j)  +/-  (1.85e-481, 1.85e-481j)
| (0.99306845695492629564 + 2.1580973195210720536e-1678j)  +/-  (4.01e-480, 4.01e-480j)
| (0.95105651629515357212 - 3.2870719483488930884e-1681j)  +/-  (3.74e-481, 3.74e-481j)
| (0.92387953251128675613 + 6.0871069712740057273e-1682j)  +/-  (8.28e-482, 8.28e-482j)
| (0.93819133592248413445 + 7.809898127497445013e-1682j)  +/-  (1.88e-481, 1.88e-481j)
| (-0.92387953251128675613 - 4.9969793878117638085e-1680j)  +/-  (8.1e-482, 8.1e-482j)
| (-0.96245523645364728763 - 6.9691343023861401787e-1685j)  +/-  (6.92e-481, 6.92e-481j)
| (-0.99306845695492629564 + 4.8118066698302859007e-1718j)  +/-  (3.94e-480, 3.94e-480j)
| (0.85264016435409222152 + 5.6038513542257450561e-1746j)  +/-  (1.19e-483, 1.19e-483j)
| (-0.99922903624072293474 - 7.9131282147961017775e-1759j)  +/-  (5.67e-480, 5.67e-480j)
| (-0.95105651629515357212 + 1.9613820109978093688e-1787j)  +/-  (3.91e-481, 3.91e-481j)
| (-0.89100652418836786236 + 8.5572230902551528984e-1798j)  +/-  (1.21e-482, 1.21e-482j)
| (0.99922903624072293474 + 1.1804216165329143051e-1792j)  +/-  (5.54e-480, 5.54e-480j)
| (0.83146961230254523708 - 2.4719221650986011349e-1804j)  +/-  (3.32e-484, 3.32e-484j)
| (0.89100652418836786236 - 3.5842658873276642676e-1801j)  +/-  (1.17e-482, 1.17e-482j)
| (-0.98768834059513772619 - 7.3364547786345739081e-1810j)  +/-  (2.82e-480, 2.82e-480j)
| (-0.8090169943749474241 + 2.6915011955551674533e-1826j)  +/-  (8.18e-485, 8.18e-485j)
| (-0.23344536385590541177 - 3.2351634452704267327e-1844j)  +/-  (1.35e-502, 1.35e-502j)
| (1 + 5.2204999990248566619e-1819j)  +/-  (2.86e-480, 2.86e-480j)
| (0.78531693088074492747 + 3.3671754885410392225e-1830j)  +/-  (1.79e-485, 1.79e-485j)
| (-0.45399049973954679156 - 8.7858303002599478335e-1841j)  +/-  (2.38e-495, 2.38e-495j)
| (-0.85264016435409222152 + 1.8042322152782114602e-1829j)  +/-  (1.24e-483, 1.24e-483j)
| (-0.78531693088074492747 - 4.9686934509701005959e-1831j)  +/-  (1.83e-485, 1.83e-485j)
| (0.98768834059513772619 - 1.104627777407463402e-1822j)  +/-  (2.96e-480, 2.96e-480j)
| (0.76040596560003093817 + 4.3508251948679611968e-1841j)  +/-  (4.01e-486, 4.01e-486j)
| (0.8090169943749474241 - 1.1914720617195964342e-1838j)  +/-  (8.45e-485, 8.45e-485j)
| (0.98078528040323044913 + 4.0236818975785409768e-1833j)  +/-  (2.06e-480, 2.06e-480j)
| (-0.61909394930983398694 + 3.300229516456590233e-1854j)  +/-  (3.02e-490, 3.02e-490j)
| (-0.83146961230254523708 - 1.8529822465577151408e-1843j)  +/-  (3.24e-484, 3.24e-484j)
| (0.52249856471594886499 - 1.2553487259285434821e-1862j)  +/-  (4.1e-493, 4.1e-493j)
| (0.67880074553294174139 + 3.2249373309432751201e-1857j)  +/-  (1.56e-488, 1.56e-488j)
| (-1 - 4.2809405023706031014e-1845j)  +/-  (4.8e-480, 4.8e-480j)
| (-0.7071067811865475244 + 3.1030004338448973651e-1880j)  +/-  (1.44e-487, 1.44e-487j)
| (-0.73432250943568553564 - 3.0849217949040439883e-1878j)  +/-  (7.63e-487, 7.63e-487j)
| (0.9969173337331279762 + 2.3045258347343101251e-1868j)  +/-  (4.82e-480, 4.82e-480j)
| (0.58778525229247312917 + 2.6290430193876862653e-1885j)  +/-  (3.49e-491, 3.49e-491j)
| (0.73432250943568553564 + 1.0764706042920178362e-1880j)  +/-  (7.65e-487, 7.65e-487j)
| (0.55557023301960222474 + 3.1049670060098992055e-1886j)  +/-  (4.14e-492, 4.14e-492j)
| (-0.58778525229247312917 - 1.8890075717678212516e-1886j)  +/-  (3.42e-491, 3.42e-491j)
| (-0.19509032201612826785 - 1.3164203410779682914e-1898j)  +/-  (6.9e-504, 6.9e-504j)
| (0.7071067811865475244 + 8.5640756890654526627e-1881j)  +/-  (9.48e-488, 9.48e-488j)
| (0.61909394930983398694 - 2.7778727300301573368e-1884j)  +/-  (2.93e-490, 2.93e-490j)
| (-0.87249600707279711453 + 2.1175475069136062301e-1877j)  +/-  (4.09e-483, 4.09e-483j)
| (-0.64944804833018365573 + 3.0519578580316895849e-1883j)  +/-  (2.28e-489, 2.28e-489j)
| (-0.67880074553294174139 - 1.6876190835214643812e-1883j)  +/-  (1.55e-488, 1.55e-488j)
| (0.90814317382508129926 - 8.1996614003350862351e-1874j)  +/-  (3.26e-482, 3.26e-482j)
| (0.45399049973954679156 - 1.4155052540652840878e-1889j)  +/-  (2.43e-495, 2.43e-495j)
| (0.96245523645364728763 + 1.4866209233987539818e-1873j)  +/-  (6.97e-481, 6.97e-481j)
| (-0.76040596560003093817 + 1.4611017576497076443e-1886j)  +/-  (4.09e-486, 4.09e-486j)
| (-0.52249856471594886499 - 3.7673547173206073996e-1894j)  +/-  (4.09e-493, 4.09e-493j)
| (3.4650324011905387068e-1928 + 1.5039041780509767537e-1928j)  +/-  (3.06e-1926, 3.06e-1926j)
| (0.64944804833018365573 - 3.7576090962123191636e-1892j)  +/-  (2.36e-489, 2.36e-489j)
| (0.48862124149695494742 - 3.7212034036642834689e-1897j)  +/-  (2.51e-494, 2.51e-494j)
| (-0.9969173337331279762 - 1.5754297345590193333e-1882j)  +/-  (4.65e-480, 4.65e-480j)
| (-0.48862124149695494742 + 2.7363805412557236672e-1912j)  +/-  (2.5e-494, 2.5e-494j)
| (-0.90814317382508129926 - 1.6510998380587871923e-1900j)  +/-  (3.25e-482, 3.25e-482j)
| (0.97236992039767660183 + 4.2803484436294767036e-1899j)  +/-  (1.23e-480, 1.23e-480j)
| (0.41865973753742808668 + 1.8884304451985606746e-1918j)  +/-  (1.9e-496, 1.9e-496j)
| (0.11753739745783764411 + 1.13024888808053139e-1927j)  +/-  (1.63e-506, 1.63e-506j)
| (-0.55557023301960222474 + 1.6099329663148409413e-1914j)  +/-  (3.92e-492, 3.92e-492j)
| (-0.38268343236508977173 + 1.3161034389580463318e-1919j)  +/-  (1.4e-497, 1.4e-497j)
| (0.87249600707279711453 + 2.5788423538382785988e-1925j)  +/-  (4.27e-483, 4.27e-483j)
| (0.38268343236508977173 + 3.9875574740191097546e-1941j)  +/-  (1.38e-497, 1.38e-497j)
| (0.27144044986507425334 + 7.0721528177895962415e-1945j)  +/-  (3.04e-501, 3.04e-501j)
| (-0.039259815759068609021 + 1.4900386654828409256e-1953j)  +/-  (1.23e-509, 1.23e-509j)
| (-0.41865973753742808668 - 4.8074774231389808e-1940j)  +/-  (1.87e-496, 1.87e-496j)
| (-0.15643446504023086901 + 7.5892840335977438145e-1950j)  +/-  (3.16e-505, 3.16e-505j)
| (0.23344536385590541177 + 1.6669177908025514051e-1946j)  +/-  (1.35e-502, 1.35e-502j)
| (0.34611705707749297647 - 1.7163377606863147542e-1942j)  +/-  (7.17e-499, 7.17e-499j)
| (0.039259815759068609021 + 5.7558656975475530739e-1953j)  +/-  (1.23e-509, 1.23e-509j)
| (-0.34611705707749297647 + 2.4465581321965479784e-1942j)  +/-  (7.11e-499, 7.11e-499j)
| (-0.3090169943749474241 - 6.6891700048760830252e-1944j)  +/-  (4.75e-500, 4.75e-500j)
| (0.078459095727844945033 + 2.1507351874131839141e-1952j)  +/-  (5.74e-508, 5.74e-508j)
| (0.3090169943749474241 + 4.2009136255932752958e-1944j)  +/-  (4.75e-500, 4.75e-500j)
| (0.19509032201612826785 + 1.9579888646184687642e-1947j)  +/-  (6.71e-504, 6.71e-504j)
| (-0.11753739745783764411 - 6.1182496656164156393e-1952j)  +/-  (1.66e-506, 1.66e-506j)
| (-0.27144044986507425334 + 1.0161651009728163737e-1945j)  +/-  (2.86e-501, 2.86e-501j)
| (-0.078459095727844945033 + 1.0432831901874717294e-1952j)  +/-  (5.74e-508, 5.74e-508j)
| (0.15643446504023086901 - 8.2814938090028124318e-1950j)  +/-  (2.97e-505, 2.97e-505j)
-------------------------------------------------
The weights are:
| (0.0125 - 2.8975871925321086086e-1663j)  +/-  (1.18e-142, 3.55e-374j)
| (0.0125 - 2.6723385448483994713e-1662j)  +/-  (9.15e-143, 2.74e-374j)
| (0.0125 + 5.2797856709204445077e-1663j)  +/-  (2.08e-143, 6.24e-375j)
| (0.0125 + 1.139329098020844313e-1664j)  +/-  (2.33e-144, 6.96e-376j)
| (0.0125 - 1.1641061923624840411e-1664j)  +/-  (1.67e-144, 4.99e-376j)
| (0.0125 - 1.1807164089699554009e-1664j)  +/-  (5.34e-145, 1.6e-376j)
| (0.0125 + 1.1719105793507038662e-1664j)  +/-  (1.08e-144, 3.23e-376j)
| (0.0125 - 3.9519188604687080984e-1663j)  +/-  (1.62e-145, 4.85e-377j)
| (0.0125 + 1.2268759047541686583e-1662j)  +/-  (2.97e-145, 8.9e-377j)
| (0.0125 - 1.8308529753083030277e-1662j)  +/-  (9.73e-147, 2.91e-378j)
| (0.0125 - 1.2265941899146123522e-1664j)  +/-  (1.47e-149, 4.39e-381j)
| (0.0125 - 1.2193118610845331816e-1662j)  +/-  (2.26e-147, 6.76e-379j)
| (0.0125 - 7.5646231252655651387e-1663j)  +/-  (3.96e-146, 1.19e-377j)
| (0.0125 - 2.5049010305832364357e-1663j)  +/-  (1.3e-148, 3.9e-380j)
| (0.0125 + 1.1357842109052553352e-1664j)  +/-  (1.63e-151, 4.89e-383j)
| (0.0125 + 1.2409231213709824253e-1664j)  +/-  (1.72e-151, 5.14e-383j)
| (0.0125 - 1.2014525294279702711e-1664j)  +/-  (6.46e-151, 1.93e-382j)
| (0.0125 + 3.257785653563581808e-1662j)  +/-  (3e-147, 8.98e-379j)
| (0.0125 - 1.3092457555123152258e-1663j)  +/-  (2.65e-152, 7.93e-384j)
| (0.0125 - 3.009164836246067048e-1664j)  +/-  (1.08e-155, 3.23e-387j)
| (0.00625 - 5.6767106976705988906e-1665j)  +/-  (8.6e-152, 2.58e-383j)
| (0.0125 + 1.273351555644554324e-1664j)  +/-  (1.03e-153, 3.1e-385j)
| (0.0125 - 4.2689659801617010823e-1664j)  +/-  (1.46e-155, 4.37e-387j)
| (0.0125 - 1.7549392921559150824e-1663j)  +/-  (6.06e-152, 1.81e-383j)
| (0.0125 + 1.1505028820253929294e-1663j)  +/-  (4.7e-153, 1.41e-384j)
| (0.0125 - 1.1424430453213960371e-1664j)  +/-  (3.04e-153, 9.1e-385j)
| (0.0125 - 1.2915692077604195803e-1664j)  +/-  (2.1e-155, 6.3e-387j)
| (0.0125 - 1.2564901888114651771e-1664j)  +/-  (3.39e-154, 1.01e-385j)
| (0.0125 + 1.1464634732703075331e-1664j)  +/-  (7.19e-154, 2.15e-385j)
| (0.0125 + 6.217646935933695904e-1664j)  +/-  (3.25e-157, 9.73e-389j)
| (0.0125 + 1.5061172226870054553e-1663j)  +/-  (2.22e-153, 6.65e-385j)
| (0.0125 - 1.4959709740744003727e-1664j)  +/-  (1.4e-159, 4.18e-391j)
| (0.0125 + 1.3550782924136479233e-1664j)  +/-  (5.05e-158, 1.51e-389j)
| (0.00625 + 5.8519433850738395664e-1663j)  +/-  (4.4e-152, 1.32e-383j)
| (0.0125 - 8.2171928093827453211e-1664j)  +/-  (4.86e-157, 1.46e-388j)
| (0.0125 + 9.1245788834767789598e-1664j)  +/-  (1.65e-156, 4.93e-388j)
| (0.0125 - 1.1371118094983347257e-1664j)  +/-  (1e-153, 3e-385j)
| (0.0125 - 1.4337060089026977173e-1664j)  +/-  (8e-160, 2.4e-391j)
| (0.0125 + 1.3112114652366155994e-1664j)  +/-  (9.37e-158, 2.8e-389j)
| (0.0125 + 1.4637686254618938407e-1664j)  +/-  (2.35e-160, 7.02e-392j)
| (0.0125 - 5.7223125593768464825e-1664j)  +/-  (3.77e-161, 1.13e-392j)
| (0.0125 + 2.8622673133377638371e-1664j)  +/-  (4.94e-164, 1.48e-395j)
| (0.0125 - 1.332353560587512417e-1664j)  +/-  (1.02e-158, 3.05e-390j)
| (0.0125 + 1.4056492242392600442e-1664j)  +/-  (4.77e-160, 1.43e-391j)
| (0.0125 + 2.0767236884668692535e-1663j)  +/-  (4.65e-158, 1.39e-389j)
| (0.0125 - 6.7872511104879996975e-1664j)  +/-  (2.27e-161, 6.8e-393j)
| (0.0125 + 7.4469674318765047367e-1664j)  +/-  (5.53e-161, 1.66e-392j)
| (0.0125 + 1.1905527671832332923e-1664j)  +/-  (4.48e-160, 1.34e-391j)
| (0.0125 - 1.5674010038322326626e-1664j)  +/-  (3.13e-166, 9.36e-398j)
| (0.0125 + 1.1572777423563277476e-1664j)  +/-  (3.37e-160, 1.01e-391j)
| (0.0125 - 1.0204537559104664078e-1663j)  +/-  (5.98e-161, 1.79e-392j)
| (0.0125 - 4.907122375551595386e-1664j)  +/-  (1.71e-165, 5.11e-397j)
| (0.0125 - 2.2929269461590665213e-1664j)  +/-  (2.3e-170, 6.9e-402j)
| (0.0125 - 1.3794767647637424426e-1664j)  +/-  (5.89e-163, 1.76e-394j)
| (0.0125 + 1.5304607435482510812e-1664j)  +/-  (8.21e-166, 2.46e-397j)
| (0.0125 + 1.3940376851676570784e-1662j)  +/-  (7.92e-161, 2.37e-392j)
| (0.0125 + 4.5693484677944687493e-1664j)  +/-  (4.63e-167, 1.39e-398j)
| (0.0125 + 3.0958201699106675915e-1663j)  +/-  (1.16e-161, 3.47e-393j)
| (0.0125 - 1.1514031231533496569e-1664j)  +/-  (2.11e-162, 6.32e-394j)
| (0.0125 + 1.6069720276444751469e-1664j)  +/-  (9.39e-169, 2.81e-400j)
| (0.0125 + 2.0475485421940709619e-1664j)  +/-  (1.17e-172, 3.52e-404j)
| (0.0125 + 5.288780372841235916e-1664j)  +/-  (1.48e-166, 4.43e-398j)
| (0.0125 - 3.7600101132034248341e-1664j)  +/-  (3.06e-170, 9.16e-402j)
| (0.0125 + 1.2134526007371176063e-1664j)  +/-  (2.56e-164, 7.67e-396j)
| (0.0125 - 1.6493733790761015093e-1664j)  +/-  (2.03e-170, 6.08e-402j)
| (0.0125 + 1.7958974517426230807e-1664j)  +/-  (9.36e-173, 2.8e-404j)
| (0.0125 + 2.38853762564065919e-1664j)  +/-  (7.76e-174, 2.32e-405j)
| (0.0125 + 4.0006525691825642877e-1664j)  +/-  (7.01e-171, 2.1e-402j)
| (0.0125 - 2.7280484907382167631e-1664j)  +/-  (1.3e-173, 3.89e-405j)
| (0.0125 - 1.8520937588008117713e-1664j)  +/-  (5.81e-174, 1.74e-405j)
| (0.0125 + 1.6948263142697679398e-1664j)  +/-  (1.14e-172, 3.42e-404j)
| (0.0125 + 2.2046760543455917727e-1664j)  +/-  (1.19e-174, 3.56e-406j)
| (0.0125 + 3.5433773344385882807e-1664j)  +/-  (9.15e-174, 2.74e-405j)
| (0.0125 - 3.3476855699479463539e-1664j)  +/-  (2.44e-174, 7.3e-406j)
| (0.0125 - 2.1230879753192157e-1664j)  +/-  (1.64e-175, 4.91e-407j)
| (0.0125 - 1.7435765481180004044e-1664j)  +/-  (7.64e-175, 2.29e-406j)
| (0.0125 + 1.9125058750519621865e-1664j)  +/-  (6.74e-176, 2.02e-407j)
| (0.0125 + 2.6051254131746575648e-1664j)  +/-  (1.03e-176, 3.1e-408j)
| (0.0125 + 3.1703466363996403693e-1664j)  +/-  (1.91e-176, 5.73e-408j)
| (0.0125 - 2.4923016044096780966e-1664j)  +/-  (7.84e-177, 2.38e-408j)
| (0.0125 - 1.9775149059332235735e-1664j)  +/-  (7.06e-177, 2.04e-408j)
